We give from first principles the non-relativistic limit of scalar and Dirac fields in curved spacetime. We aim to find general relativistic corrections to the quantum theory of particles affected by Newtonian gravity, a regime nowadays experimentally accessible. We believe that the ever-improving measurement accuracy and the theoretical interest in finding general relativistic effects in quantum systems require the introduction of corrections to the Schrödinger-Newtonian theory. We rigorously determine these corrections by the non-relativistic limit of fully relativistic quantum theories in curved spacetime. For curved static spacetimes, we show how a non-inertial observer (equivalently, an observer in the presence of a gravitational field) can distinguish a scalar field from a Dirac field by particle-gravity interaction. We study the Rindler spacetime and discuss the difference between the resulting non-relativistic Hamiltonians. We find that for sufficiently large acceleration, the gravity-spin coupling dominates over the corrections for scalar fields, promoting Dirac particles as the best candidates for observing non-Newtonian gravity in quantum particle phenomenology.
Quantum field theory beyond Minkowski is still largely unexplored, and the links with quantum information are surprising.
We know that the Minkowski vacuum appears as a thermal state in a uniformly accelerated frame (Rindler/Unruh) or in the proximity of a black hole (Hawking).
Beyond Unruh and Hawking radiation, how do quantum states appear to a noninertial observer? We derive a general technique to understand the way acceleration alters Minkowski-Fock states. It turns out that one can use and engineer quantum correlations to measure acceleration. But a lot of work is still needed with advanced mathematical approaches, although these new general results may be useful for many applications.
An explicit Wigner formulation of Minkowski particle states for non-inertial observers is unknown. Here, we derive a general prescription to compute the characteristic function for Minkowski-Fock states in accelerated frames. For the special case of single-particle and two-particle states, this method enables to derive mean values of particle numbers and correlation function in the momentum space, and the way they are affected by the acceleration of the observer. We show an indistinguishability between Minkowski single-particle and two-particle states in terms of Rindler particle distribution that can be regarded as a way for the observer to detect any acceleration of the frame. We find that for two-particle states the observer is also able to detect acceleration by measuring the correlation between Rindler particles with different momenta.
We show that Minkowski single-particle states localized beyond the horizon modify the Unruh thermal distribution in an accelerated frame. This means that, contrary to classical predictions, accelerated observers can reveal particles emitted beyond the horizon. The method we adopt is based on deriving the explicit Wigner characteristic function for the complete description of the quantum field in the non-inertial frame and can be generalized to general states
From condensed matter to quantum chromodynamics, multidimensional spins are a fundamental paradigm, with a pivotal role in combinatorial optimization and machine learning. Machines formed by coupled parametric oscillators can simulate spin models, but only for Ising or low-dimensional spins. Currently, machines implementing arbitrary dimensions remain a challenge. Here, we introduce and validate a hyperspin machine to simulate multidimensional continuous spin models. We realize high-dimensional spins by pumping groups of parametric oscillators, and study NP-hard graphs of hyperspins. The hyperspin machine can interpolate between different dimensions by tuning the coupling topology, a strategy that we call “dimensional annealing”. When interpolating between the XY and the Ising model, the dimensional annealing impressively increases the success probability compared to conventional Ising simulators. Hyperspin machines are a new computational model for combinatorial optimization. They can be realized by off-the-shelf hardware for ultrafast, large-scale applications in classical and quantum computing, condensed-matter physics, and fundamental studies.
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